Kinetic studies employing classical techniques

In contrast, with [Pd(allyl)(MeCN)2]+ (Fig. 12.2,graph ii), there is a rather variable induction period, a much less pronounced accumulation-depletion phase, non-linear (complex) evolution, and lower selectivity for 13upon isomerisation of 11 (13 12 2 1). Amajor complication is the slow induction phase which gives rise to a trickle-feed of active catalyst and, consequently, this system is far harder to analyse. Nonetheless, with both systems, the sole 

With pro-catalysts of type B, the evolution profiles (Fig. 12.3) are very different the product is 12 instead of 11 and this does not undergo the extreme accumulation-depletion cycles observed with pro-catalysts of type A, which give 11 as the initial product. With the [(phen)Pd(Me)(MeCN)]+ system, clean pseudo-zero-order kinetics are again observed for the first 75% of reaction (k0bs = 7.1 x 10 7 M s 1) and the co-products (11 and 13) are formed at a level of ca 5% throughout the evolution (Fig. 12.3, graph Hi). 

With the neutral [(RCN)2PdCl2] pro-catalyst system (Fig. 12.3, graph iv), computer simulation of the kinetic data acquired with various initial pro-catalyst concentrations and substrate concentrations resulted in the conclusion that the turnover rates are controlled by substrate-induced trickle feed catalyst generation, substrate concentration-dependent turnover and continuous catalyst termination. The active catalyst concentration is always low and, for a prolonged phase in the middle of the reaction, the net effect is to give rise to an apparent pseudo-zero-order kinetic profile. For both sets of data obtained with pro-catalysts of type B (Fig. 12.3), one could conceive that the kinetic product is 11, but (unlike with type A) the isomerisation to 12 is extremely rapid such that 11 does not accumulate appreciably. Of course, in this event, one needs to explain why the isomerisation of 11 now proceeds to give 12 rather than 13. With the [(phen)Pd(Me)(MeCN)]+ system, analysis of the relative concentrations of 11 and 13 as the conversion proceeds confirmed that the small amount of 

11 that is generated isomerises predominantly to 13. With the [(RCN)2PdCl2] pro-catalyst system, spiking the reaction with 11 results in strong inhibition and its slow isomerisation to 13, not 12. 

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In Chapter 2, several types of kinetic schemes were examined in detail. While the mathematical apparatus was developed to describe these cases, little was said about other methods used in kinetic studies or about experimental techniques. In this chapter, we will describe some of the methods employed in the study of kinetics that do not make use of the integrated rate laws. In some cases, the exact rate law may be unknown, and some of the experimental techniques do not make use of the classical determination of concentration as a function of time to get data to fit to a rate law. A few of the techniques described in this chapter are particularly useful in such cases. 

Theoretical studies of the properties of the individual components of nanocat-alytic systems (including metal nanoclusters, finite or extended supporting substrates, and molecular reactants and products), and of their assemblies (that is, a metal cluster anchored to the surface of a solid support material with molecular reactants adsorbed on either the cluster, the support surface, or both), employ an arsenal of diverse theoretical methodologies and techniques for a recent perspective article about computations in materials science and condensed matter studies [254], These theoretical tools include quantum mechanical electronic structure calculations coupled with structural optimizations (that is, determination of equilibrium, ground state nuclear configurations), searches for reaction pathways and microscopic reaction mechanisms, ab initio investigations of the dynamics of adsorption and reactive processes, statistical mechanical techniques (quantum, semiclassical, and classical) for determination of reaction rates, and evaluation of probabilities for reactive encounters between adsorbed reactants using kinetic equation for multiparticle adsorption, surface diffusion, and collisions between mobile adsorbed species, as well as explorations of spatiotemporal distributions of reactants and products. 

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